Boundary Element Methods in Probabilistic Acoustic Scattering Problems

1990 ◽  
pp. 529-535
Author(s):  
Raymond P. Daddazio ◽  
Mohammed M. Ettouney
Keyword(s):  
Boundary Element ◽  
Acoustic Scattering ◽  
Boundary Element Methods ◽  
Scattering Problems ◽  
Acoustic Scattering Problems

Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems

2020 ◽  
Vol 28 (4) ◽  
pp. 223-245
Author(s):  
Gabriel N. Gatica ◽  
Salim Meddahi
Keyword(s):  
Boundary Element ◽  
Acoustic Scattering ◽  
Rates Of Convergence ◽  
Boundary Element Methods ◽  
Scattering Problems ◽  
Combined Use ◽  
Virtual Element ◽  
2D And 3D ◽  
Element Method ◽  
Acoustic Scattering Problems

AbstractThis paper extends the applicability of the combined use of the virtual element method (VEM) and the boundary element method (BEM), recently introduced to solve the coupling of linear elliptic equations in divergence form with the Laplace equation, to the case of acoustic scattering problems in 2D and 3D. The well-posedness of the continuous and discrete formulations are established, and then Cea-type estimates and consequent rates of convergence are derived.

Adaptivity and Three Dimensional Hierarchical Boundary Elements for Rigid Acoustic Scattering Problems

1995 ◽  
Author(s):  
Steven J. Newhouse ◽  
Ian C. Mathews
Keyword(s):  
Boundary Element ◽  
Acoustic Analysis ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Error Estimator ◽  
Infinite Domain ◽  
Scattering Problems ◽  
Effective Form ◽  
Mesh Density ◽  
Acoustic Scattering Problems

Abstract The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited. This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.

Newton-Like Method for Solving Inverse Obstacle Acoustic Scattering Problems

2000 ◽  
Author(s):  
Rabia Djellouli ◽  
Charbel Farhat ◽  
Radek Tezaur
Keyword(s):  
Acoustic Scattering ◽  
Numerical Procedure ◽  
Decomposition Methods ◽  
Computationally Efficient ◽  
Scattering Problems ◽  
Absorbing Boundary ◽  
Element Discretization ◽  
Jacobian Matrices ◽  
Fast Solution ◽  
Acoustic Scattering Problems

Abstract A Newton-like method is designed for determining the shape or sought-after shape modifications of a scatterer from the knowledge of acoustic far-field patterns at a given number of observation points. This method distinguishes itself from existing numerical procedures by the following features: (a) exact Jacobian matrices for the linearized problems rather than approximate ones, (b) a fast numerical procedure for computing these Jacobian matrices, (c) a computationally efficient absorbing boundary condition for the finite element discretization, and (d) a numerically scalable domain decomposition methods for the fast solution of high-frequency direct acoustic scattering problems.

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